A proof of Pesin's formula

Abstract

Let f: M → M be a diffeomorphism of a compact manifold M and let χ:M → R be defined by putting χ(x) equal to the sum of the non-negative characteristic exponents of f at x, each being counted with its multiplicity. If μ is an f-invariant probability of M which is absolutely continuous relative to Lebesgue measure, then Pesin has proved the entropy, h_μ(f), is given by We prove this formula without using the theory of stable manifolds.